In a transportation problem, generally, a single criterion of minimizing the total cost is considered. But in certain practical situations two or more objectives are relevant. For example, the objectives may be minimizations of total cost, consumption of certain scarce resources such as energy, total deterioration of goods during transportation, etc. Clearly, this problem can be solved using any of the multiobjective linear programming techniques; but the computational efforts needed would be prohibitive in many cases. The computational complexity in these techniques arises from the fact that each of the methods finds the set of nondominated extreme points in the solution space where such extreme points are, generally, many. Therefore, this paper develops a method of finding the nondominated extreme points in the criteria space. Such extreme points in the criteria space would be generally less and only these are needed while choosing a nondominated solution for implementation. The method involves a parametric search in the criteria space. Although the method is developed with respect to a bicriteria transportation problem, it is applicable to any bicriteria linear program in general. The bottleneck criterion included as a third objective is particularly significant in time bound transportation schedules. A numerical example is included.programming: multiple criteria, transportation

Certain properties of a shortest chain subject to several side constraints are established. Based on these an implicit enumeration algorithm, that is, a generalization of the one given by Dijkstra for the case without any side constraint, is presented. Validation of the algorithm and an illustrative example are included.

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In this paper, we consider two problems related to single-commodity flows on a directed network. In the first problem, for a given s −t flow, if an arc is destroyed, all the flow that is passing through that arc is destroyed. What is left flowing from s to t is the residual flow. The objective is to determine a flow pattern such that the residual flow is maximized. We provide a strongly polynomial algorithm for this problem, called the maximum residual flow problem, and consider various extensions of this basic model. In the second problem, known as the "most vital arc" problem, the objective is to remove an arc so that the maximal flow on the residual network is as small as possible. Results are also derived which help implement an efficient scheme for solving this problem.

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